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Title overview
For courses in geometry.
Every student can succeed
Elayn Martin-Gay's developmental math program is motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. Geometry, 1st Edition continues her focus on students, providing a solid foundation in Euclidean geometry for students who may not have previous experience in geometry.
Hallmark features of this title
- Objectives begin each section; these are also repeated at the point of discussion within the section. When applicable, under the list of objectives, there is a list of new Vocabulary words. Throughout the section, each new vocabulary word is highlighted at the place of the definition.
- Helpful Hints offer practical advice on applying mathematical concepts. Strategically placed, they help students avoid common trouble areas and mistakes.
- Detailed step-by-step examples provide guidance for students.
- Practice exercises are paired with each example to actively involve students in the learning process.
- Abundant exercises inlude Vocabulary, Readiness and Video Checks; Guided Applications; Mixed Practice; Concept Extension; and more. Exercise Set Resource Icons at the opening of each exercise set remind students of resources available for extra practice and support.
Key features
Features of MyLab Math for the 1st Edition
- The available Video Organizer helps students take notes and work practice exercises while watching the Interactive Lecture Series in MyLab Math. All content in the Video Organizer is presented in the same order as it is presented in the videos, making it easy for students to create a course notebook and build good study habits.
- The Interactive Lecture Series featuring Elayn Martin-Gay provides students with active learning at their own pace.
- A complete lecture for each section of the text highlights key examples and exercises from the text. Pop-ups reinforce key terms, definitions, and concepts.
- Menu navigation features allow students to quickly find and focus on the examples and exercises they need to review.
- Chapter Test Prep Videos help students during their most teachable moment–when they are preparing for a test. This innovation provides step-by-step solutions for the exercises found in each chapter test. The videos are captioned in English and Spanish.
- Extensive exercise coverage gives students the practice they need to succeed.
Table of contents
- 1. A Beginning of Geometry
- 1.1 Tips for Success in Mathematics
- 1.2 Geometry–A Mathematical System
- 1.3 Points, Lines, and Planes
- 1.4 Segments and Their Measure
- 1.5 Angles and Their Measure
- 1.6 Angle Pairs and Their Relationships
- 1.7 Coordinate Geometry–Midpoint and Distance Formulas
- 1.8 Constructions–Basic Geometry Constructions
- 2. Introduction to Reasoning and Proofs
- 2.1 Perimeter, Circumference, and Area
- 2.2 Patterns and Inductive Reasoning
- 2.3 Conditional Statements
- 2.4 Biconditional Statements and Definitions
- 2.5 Deductive Reasoning
- 2.6 Reviewing Properties of Equality and Writing Two-Column Proofs
- 2.7 Proving Theorems About Angles
- 3. Parallel and Perpendicular Lines
- 3.1 Lines and Angles
- 3.2 Proving Lines Are Parallel
- 3.3 Parallel Lines and Angles Formed by Transversals
- 3.4 Proving Theorems About Parallel and Perpendicular Lines
- 3.5 Constructions–Parallel and Perpendicular Lines
- 3.6 Coordinate Geometry–The Slope of a Line
- 3.7 Coordinate Geometry–Equations of Lines
- 4. Triangles and Congruence
- 4.1 Types of Triangles
- 4.2 Congruent Figures
- 4.3 Congruent Triangles by SSS and SAS
- 4.4 Congruent Triangles by ASA and AAS
- 4.5 Proofs Using Congruent Triangles
- 4.6 Isosceles, Equilateral, and Right Triangles
- 5. Special Properties of Triangles
- 5.1 Perpendicular and Angle Bisectors
- 5.2 Bisectors of a Triangle
- 5.3 Medians and Altitudes of a Triangle
- 5.4 Midsegments of Triangles
- 5.5 Indirect Proofs and Inequalities in One Triangle
- 5.6 Inequalities in Two Triangles
- 6. Quadrilaterals
- 6.1 Polygons
- 6.2 Parallelograms
- 6.3 Proving that a Quadrilateral Is a Parallelogram
- 6.4 Rhombuses, Rectangles, and Squares
- 6.5 Trapezoids and Kites
- 7. Similarity
- 7.1 Ratios and Proportions
- 7.2 Proportion Properties and Problem Solving
- 7.3 Similar Polygons
- 7.4 Proving Triangles Are Similar
- 7.5 Geometric Mean and Similarity in Right Triangles
- 7.6 Additional Proportions in Triangles
- 8. Transformations
- 8.1 Rigid Transformations
- 8.2 Translations
- 8.3 Reflections
- 8.4 Rotations
- 8.5 Dilations
- 8.6 Compositions of Reflections
- Extension–Frieze Patterns
- 9. Right Triangles and Trigonometry
- 9.1 The Pythagorean Theorem and Its Converse
- 9.2 Special Right Triangles
- 9.3 Trigonometric Ratios
- 9.4 Solving Right Triangles
- 9.5 Vectors
- Extension–Law of Sines
- Extension–Law of Cosines
- 10. Area
- 10.1 Angle Measures of Polygons and Regular Polygon Tessellations
- 10.2 Areas of Triangles and Quadrilaterals with a Review of Perimeter
- 10.3 Areas of Regular Polygons
- 10.4 Perimeters and Areas of Similar Figures
- 10.5 Arc Measures, Circumferences, and Arc Lengths of Circles
- 10.6 Areas of Circles and Sectors
- 10.7 Geometric Probability
- 11. Surface Area and Volume
- 11.1 Solids and Cross Sections
- 11.2 Surface Areas of Prisms and Cylinders
- 11.3 Surface Areas of Pyramids and Cones
- 11.4 Volumes of Prisms and Cylinders and Cavalieri’s Principle
- 11.5 Volumes of Pyramids and Cones
- 11.6 Surface Areas and Volumes of Spheres
- 11.7 Areas and Volumes of Similar Solids
- 12. Circles and Other Conic Sections
- 12.1 Circle Review and Tangent Lines
- 12.2 Chords and Arcs
- 12.3 Inscribed Angles
- 12.4 Additional Angle Measures and Segment Lengths
- 12.5 Coordinate Plane–Circles
- 12.6 Locus
- Extension–Parabolas
Student Success Resource Section
A. Review of Basic Concepts
- A.1 Measurement Conversions
- A.2 Probability
- A.3 Exponents, Order of Operations, and Variable Expressions
- A.4 Operations on Real Numbers
- A.5 Simplifying Expressions
- A.6 Solving Linear Equations
- A.7 Solving Linear Inequalities
- A.8 Solving Formulas for a Variable
- A.9 The Coordinate Plane
- A.10 Graphing Linear Equations
- A.11 Solving Systems of Linear Equations in Two Variables
- A.12 Exponents
- A.13 Multiplying Polynomials
- A.14 Simplifying Radical Expressions
- A.15 Solving Quadratic Equations by Factoring
- A.16 Solving Quadratic Equations by the Square Root Property
- A.17 Solving Quadratic Equations by the Quadratic Formula
Tables
- Math Symbols
- Formulas
- Measures
- Properties of Real Numbers Postulates, Theorems, and Additional Proofs
B. Additional Lessons
- B.1 Ellipses and Hyperbolas
- B.2 Measurement, Rounding Error, and Reasonableness
- B.3 The Effect of Measurement Errors on Calculations
Answers to Selected Exercises
Index
Photo Credits
Author bios
About our author
Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association’s Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators.
Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most “teachable moment”–as they prepare for a test–along with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebra, and intermediate algebra.
Elayn is the author of 12 published textbooks and numerous multimedia interactive products, all specializing in developmental mathematics courses. She has also published series in Algebra 1, Algebra 2, and Geometry. She has participated as an author across a broad range of educational materials: textbooks, videos, tutorial software, and courseware. This offers an opportunity for multiple combinations for an integrated teaching and learning package, offering great consistency for the student.